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This is always the case with bracketing commas, and it gives you a simple way of checking your punctuation. If you have set off some words with a pair of bracketing commas, and you find you can't remove those words without destroying the sentence, you have done something wrong. Here is an example of wrong use, taken from Carey (1958):

*Yet, outside that door, lay a whole new world.

If you try to remove the words outside that door, the result is *Yet lay a whole new world, which is not a sentence. The problem here is that outside that door is not an interruption at all: it's an essential part of the sentence. So, the bracketing commas shouldn't be there. Just get rid of them:

Yet outside that door lay a whole new world.

Is this a common rule?

**In this example from a published review the isolated information does damage the sentence when removed and or leaves something ungrammatical.*
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Is there any right or wrong in this? It looks and sounds wrong to me eitherway. I think the sentence should flow when the information is removed.

[It] faithfully adopted much of what so resonated in the original genre-creating film, the stoic killer, the gruesome executions, the suburban nightmares, what makes his version such a thrill is how it deviates from its long-ago predecessor.

It is true that removing any adverbial phrase should still leave a grammatical sentence. You must be careful about removing commas, however, because adverbial phrases can be chained or nested, and we don't give as much information with commas as we could, for example, with parentheses. In your first example 'yet' is also adverbial, but it can stand without a comma because of its temporal quality. If 'yet' was replaced by a non-temporal adverb (like 'however') then it would need bracketing comma[s] too.

In your second example, the sentence shown is poorly punctuated. The commas that bracket the bold list should be changed to ':' and ';' respectively.

This is commonly accepted, yes.

If you cannot remove parenthetical information without something grammatical resulting, then it should be considered essential to the sentence and not presented parenthetically in the first place.

But you have to be careful about what you consider to be bracketing commas. Sometimes you'll find what looks like a pair of commas that aren't actually a comma pair but two sequential single commas. You have to look at the sentence to determine how they are being used.

For instance, your last paragraph is not an example of parenthetical (bracketed) information; it's a use of sequential single commas that indicate items in a list.

The use of the final comma is simply ungrammatical because it precedes a second independent clause. (Which makes it a comma splice.) Unless something different was intended (in which case it should have been rephrased), it should have been punctuated differently.

Some people would also argue that it would be stylistically more appropriate to replace the first comma with a colon—and that there should be a conjunction before the final list item.

For instance, the following takes all of that into consideration:

[It] faithfully adopted much of what so resonated in the original genre-creating film: the stoic killer, the gruesome executions, and the suburban nightmares. What makes his version such a thrill is how it deviates from its long-ago predecessor.

A semicolon could also have been used rather than turning it into two sentences.